Neural architecture construction using envelopenets for image recognition

ABSTRACT

In one embodiment, a device forms a neural network envelope cell that comprises a plurality of convolution-based filters in series or parallel. The device constructs a convolutional neural network by stacking copies of the envelope cell in series. The device trains, using a training dataset of images, the convolutional neural network to perform image classification by iteratively collecting variance metrics for each filter in each envelope cell, pruning filters with low variance metrics from the convolutional neural network, and appending a new copy of the envelope cell into the convolutional neural network.

RELATED APPLICATION

This application claims priority to U.S. Provisional Patent Appl. No.62/643,839, filed on Mar. 16, 2018, entitled NEURAL ARCHITECTURECONSTRUCTION USING ENVELOPENETS, by Kamath, et al., the contents ofwhich are incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates generally to computer networks, and, moreparticularly, to neural architecture construction using EnvelopeNets forimage recognition.

BACKGROUND

Interest in machine learning has increased considerably in recent years.From image recognition and analysis, to personal assistants, todiagnostic systems, machine learning is becoming more and more integralto many technologies. One form of machine learning that is of particularinterest in the field of image recognition is the convolutional neuralnetwork.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments herein may be better understood by referring to thefollowing description in conjunction with the accompanying drawings inwhich like reference numerals indicate identically or functionallysimilar elements, of which:

FIGS. 1A-1B illustrate an example communication network;

FIG. 2 illustrates an example network device/node;

FIGS. 3A-3D illustrate example cells for a neural network;

FIGS. 4A-4B illustrate the construction and training of a neuralnetwork;

FIG. 5 illustrates an example plot of accuracy test results using thetechniques herein; and

FIG. 6 illustrates an example simplified procedure for training a neuralnetwork using envelope cells.

DESCRIPTION OF EXAMPLE EMBODIMENTS Overview

According to one or more embodiments of the disclosure, a device forms aneural network envelope cell that comprises a plurality ofconvolution-based filters in series or parallel. The device constructs aconvolutional neural network by stacking copies of the envelope cell inseries. The device trains, using a training dataset of images, theconvolutional neural network to perform image classification byiteratively collecting variance metrics for each filter in each envelopecell, pruning filters with low variance metrics from the convolutionalneural network, and appending a new copy of the envelope cell into theconvolutional neural network.

DESCRIPTION

A computer network is a geographically distributed collection of nodesinterconnected by communication links and segments for transporting databetween end nodes, such as personal computers and workstations, or otherdevices, such as sensors, etc. Many types of networks are available,with the types ranging from local area networks (LANs) to wide areanetworks (WANs). LANs typically connect the nodes over dedicated privatecommunications links located in the same general physical location, suchas a building or campus. WANs, on the other hand, typically connectgeographically dispersed nodes over long-distance communications links,such as common carrier telephone lines, optical lightpaths, synchronousoptical networks (SONET), or synchronous digital hierarchy (SDH) links,or Powerline Communications (PLC) such as IEEE 61334, IEEE P1901.2, andothers. The Internet is an example of a WAN that connects disparatenetworks throughout the world, providing global communication betweennodes on various networks. The nodes typically communicate over thenetwork by exchanging discrete frames or packets of data according topredefined protocols, such as the Transmission Control Protocol/InternetProtocol (TCP/IP). In this context, a protocol consists of a set ofrules defining how the nodes interact with each other. Computer networksmay further be interconnected by an intermediate network node, such as arouter, to extend the effective “size” of each network.

Smart object networks, such as sensor networks, in particular, are aspecific type of network having spatially distributed autonomous devicessuch as sensors, actuators, etc., that cooperatively monitor physical orenvironmental conditions at different locations, such as, e.g.,energy/power consumption, resource consumption (e.g., water/gas/etc. foradvanced metering infrastructure or “AMI” applications) temperature,pressure, vibration, sound, radiation, motion, pollutants, etc. Othertypes of smart objects include actuators, e.g., responsible for turningon/off an engine or perform any other actions. Sensor networks, a typeof smart object network, are typically shared-media networks, such aswireless networks. That is, in addition to one or more sensors, eachsensor device (node) in a sensor network may generally be equipped witha radio transceiver or other communication port, a microcontroller, andan energy source, such as a battery. Often, smart object networks areconsidered field area networks (FANs), neighborhood area networks(NANs), personal area networks (PANs), etc. Generally, size and costconstraints on smart object nodes (e.g., sensors) result incorresponding constraints on resources such as energy, memory,computational speed and bandwidth.

FIG. 1A is a schematic block diagram of an example computer network 100illustratively comprising nodes/devices, such as a plurality ofrouters/devices interconnected by links or networks, as shown. Forexample, customer edge (CE) routers 110 may be interconnected withprovider edge (PE) routers 120 (e.g., PE-1, PE-2, and PE-3) in order tocommunicate across a core network, such as an illustrative networkbackbone 130. For example, routers 110, 120 may be interconnected by thepublic Internet, a multiprotocol label switching (MPLS) virtual privatenetwork (VPN), or the like. Data packets 140 (e.g., traffic/messages)may be exchanged among the nodes/devices of the computer network 100over links using predefined network communication protocols such as theTransmission Control Protocol/Internet Protocol (TCP/IP), User DatagramProtocol (UDP), Asynchronous Transfer Mode (ATM) protocol, Frame Relayprotocol, or any other suitable protocol. Those skilled in the art willunderstand that any number of nodes, devices, links, etc. may be used inthe computer network, and that the view shown herein is for simplicity.

In some implementations, a router or a set of routers may be connectedto a private network (e.g., dedicated leased lines, an optical network,etc.) or a virtual private network (VPN), such as an MPLS VPN, thanks toa carrier network, via one or more links exhibiting very differentnetwork and service level agreement characteristics. For the sake ofillustration, a given customer site may fall under any of the followingcategories:

1.) Site Type A: a site connected to the network (e.g., via a private orVPN link) using a single CE router and a single link, with potentially abackup link (e.g., a 3G/4G/LTE backup connection). For example, aparticular CE router 110 shown in network 100 may support a givencustomer site, potentially also with a backup link, such as a wirelessconnection.

2.) Site Type B: a site connected to the network using two MPLS VPNlinks (e.g., from different service providers), with potentially abackup link (e.g., a 3G/4G/LTE connection). A site of type B may itselfbe of different types:

2a.) Site Type B1: a site connected to the network using two MPLS VPNlinks (e.g., from different service providers), with potentially abackup link (e.g., a 3G/4G/LTE connection).

2b.) Site Type B2: a site connected to the network using one MPLS VPNlink and one link connected to the public Internet, with potentially abackup link (e.g., a 3G/4G/LTE connection). For example, a particularcustomer site may be connected to network 100 via PE-3 and via aseparate Internet connection, potentially also with a wireless backuplink.

2c.) Site Type B3: a site connected to the network using two linksconnected to the public Internet, with potentially a backup link (e.g.,a 3G/4G/LTE connection).

Notably, MPLS VPN links are usually tied to a committed service levelagreement, whereas Internet links may either have no service levelagreement at all or a loose service level agreement (e.g., a “GoldPackage” Internet service connection that guarantees a certain level ofperformance to a customer site).

3.) Site Type C: a site of type B (e.g., types B1, B2 or B3) but withmore than one CE router (e.g., a first CE router connected to one linkwhile a second CE router is connected to the other link), andpotentially a backup link (e.g., a wireless 3G/4G/LTE backup link). Forexample, a particular customer site may include a first CE router 110connected to PE-2 and a second CE router 110 connected to PE-3.

FIG. 1B illustrates an example of network 100 in greater detail,according to various embodiments. As shown, network backbone 130 mayprovide connectivity between devices located in different geographicalareas and/or different types of local networks. For example, network 100may comprise local networks 160, 162 that include devices/nodes 10-16and devices/nodes 18-20, respectively, as well as a data center/cloudenvironment 150 that includes servers 152-154. Notably, local networks160-162 and data center/cloud environment 150 may be located indifferent geographic locations.

Servers 152-154 may include, in various embodiments, a networkmanagement server (NMS), a dynamic host configuration protocol (DHCP)server, a constrained application protocol (CoAP) server, an outagemanagement system (OMS), an application policy infrastructure controller(APIC), an application server, etc. As would be appreciated, network 100may include any number of local networks, data centers, cloudenvironments, devices/nodes, servers, etc.

The techniques herein may also be applied to other network topologiesand configurations. For example, the techniques herein may be applied topeering points with high-speed links, data centers, etc. Further, invarious embodiments, network 100 may include one or more mesh networks,such as an Internet of Things network. Loosely, the term “Internet ofThings” or “IoT” refers to uniquely identifiable objects/things andtheir virtual representations in a network-based architecture. Inparticular, the next frontier in the evolution of the Internet is theability to connect more than just computers and communications devices,but rather the ability to connect “objects” in general, such as lights,appliances, vehicles, heating, ventilating, and air-conditioning (HVAC),windows and window shades and blinds, doors, locks, etc. The “Internetof Things” thus generally refers to the interconnection of objects(e.g., smart objects), such as sensors and actuators, over a computernetwork (e.g., via IP), which may be the public Internet or a privatenetwork.

Notably, shared-media mesh networks, such as wireless networks, etc.,are often on what is referred to as Low-Power and Lossy Networks (LLNs),which are a class of network in which both the routers and theirinterconnect are constrained. In particular, LLN routers typicallyoperate with highly constrained resources, e.g., processing power,memory, and/or energy (battery), and their interconnections arecharacterized by, illustratively, high loss rates, low data rates,and/or instability. LLNs are comprised of anything from a few dozen tothousands or even millions of LLN routers, and support point-to-pointtraffic (e.g., between devices inside the LLN), point-to-multipointtraffic (e.g., from a central control point such at the root node to asubset of devices inside the LLN), and multipoint-to-point traffic(e.g., from devices inside the LLN towards a central control point).Often, an IoT network is implemented with an LLN-like architecture. Forexample, as shown, local network 160 may be an LLN in which CE-2operates as a root node for nodes/devices 10-16 in the local mesh, insome embodiments.

FIG. 2 is a schematic block diagram of an example node/device 200 thatmay be used with one or more embodiments described herein, e.g., as anyof the computing devices shown in FIGS. 1A-1B, particularly the PErouters 120, CE routers 110, nodes/device 10-20, servers 152-154 (e.g.,a network controller located in a data center, etc.), any othercomputing device that supports the operations of network 100 (e.g.,switches, etc.), or any of the other devices referenced below. Thedevice 200 may also be any other suitable type of device depending uponthe type of network architecture in place, such as IoT nodes, etc.Device 200 comprises one or more network interfaces 210, one or moreprocessors 220, and a memory 240 interconnected by a system bus 250, andis powered by a power supply 260.

The network interfaces 210 include the mechanical, electrical, andsignaling circuitry for communicating data over physical links coupledto the network 100. The network interfaces may be configured to transmitand/or receive data using a variety of different communicationprotocols. Notably, a physical network interface 210 may also be used toimplement one or more virtual network interfaces, such as for virtualprivate network (VPN) access, known to those skilled in the art.

The memory 240 comprises a plurality of storage locations that areaddressable by the processor(s) 220 and the network interfaces 210 forstoring software programs and data structures associated with theembodiments described herein. The processor 220 may comprise necessaryelements or logic adapted to execute the software programs andmanipulate the data structures 245. An operating system 242 (e.g., theInternetworking Operating System, or IOS®, of Cisco Systems, Inc.,another operating system, etc.), portions of which are typicallyresident in memory 240 and executed by the processor(s), functionallyorganizes the node by, inter alia, invoking network operations insupport of software processors and/or services executing on the device.These software processors and/or services may comprise a machinelearning process 248.

It will be apparent to those skilled in the art that other processor andmemory types, including various computer-readable media, may be used tostore and execute program instructions pertaining to the techniquesdescribed herein. Also, while the description illustrates variousprocesses, it is expressly contemplated that various processes may beembodied as modules configured to operate in accordance with thetechniques herein (e.g., according to the functionality of a similarprocess). Further, while processes may be shown and/or describedseparately, those skilled in the art will appreciate that processes maybe routines or modules within other processes.

As noted above, machine learning can be used in a variety of differenttechnologies. For example, machine learning can be used in the field ofimage recognition and analysis to identify objects depicted in stillimages and/or video. In another example, machine learning can be used ina computer network to assess the health of the network (e.g., byclassifying the operational behavior of the devices and/or networktraffic, performing root-cause analysis for certain behaviors, etc.). Ina further example, machine learning can be used for network securitypurposes, such as detecting malicious or otherwise undesired operations(e.g., traffic associated with malware, etc.).

Neural Architecture Construction Using EnvelopeNets

The techniques herein introduce a neural architecture construction using“EnvelopeNets” that constructs a neural network from a network ofsuperset cells, referred to herein as “envelope cells,” via arestructuring process. In some aspects, a superset cell can be used toconstruct the EnvelopeNet using this cell, which envelopes severalbespoke and generated cells. This technique designs a network optimizedfor a training set and resource availability by selectivelyrestructuring blocks within the cells of the EnvelopeNet based onmetrics collected during a training of the EnvelopeNet.

Specifically, according to various embodiments, a device forms a neuralnetwork envelope cell that comprises a plurality of convolution-basedfilters in series or parallel. The device constructs a convolutionalneural network by stacking copies of the envelope cell in series. Thedevice trains, using a training dataset of images, the convolutionalneural network to perform image classification by iteratively collectingvariance metrics for each filter in each envelope cell, pruning filterswith low variance metrics from the convolutional neural network, andappending a new copy of the envelope cell into the convolutional neuralnetwork.

Illustratively, the techniques described herein may be performed byhardware, software, and/or firmware, such as in accordance with themachine learning process 248, which may include computer executableinstructions executed by the processor 220 (or independent processor ofinterfaces 210) to perform functions relating to the techniquesdescribed herein.

Operationally, the techniques herein propose a neural architectureconstruction method based on EnvelopeNets that constructs a neuralnetwork from a network of superset cells (called envelope cells) via arestructuring algorithm. In various embodiments, a superset cell isdesigned that envelopes several previously proposed bespoke andgenerated cells and construct an EnvelopeNet using this cell. In someembodiments, the method designs a network optimized for a training setand resource availability by selectively restructuring blocks within thecells of the EnvelopeNet based on metrics collected during a training ofthe EnvelopeNet.

According to various embodiments, EnvelopeNet-based neural networkconstruction and training may entail stacking envelope cells, andperforming filter pruning and network restructuring, to train the neuralnetwork. Note that the envelope cells introduced herein are not optimalin any way. Indeed, the techniques herein intentionally choose envelopecells to be non-optimal and over provisioned. During model training, thefilter pruning and network restructuring techniques use extractedmetrics from the EnvelopeNet to iteratively optimize the network. Insome aspects, this may be achieved by pruning low performing filters andappending new envelope cells to the deep end of the network. In doingso, the training optimization avoids having to search over the entirespace of network architectures for the optimal architecture. The networkrestructuring method used herein also differs from other neuroevolutionmethods, where single blocks/filters are added based on a mutation or anoptimization technique.

To help illustrate the proposed neural network construction and trainingapproaches introduced herein, the following terminology is used:

-   -   Block B_(i)— An operation/operator, such as a convolution (e.g.,        a convolution-based filter), max pool, concatenation, or the        like.    -   Cell C_(i)—A combination of blocks in series or parallel. Such a        cell may be custom built or generated, in various embodiments.    -   Network N_(i)—A combination of cells and/or blocks. For example,        a network may consist of cells stacked in series or a directed        graph of blocks.    -   Network Width—The number of parallel branches of a cell.

Envelope construction can be formalized as the following problem: givena network N_(e) of depth L_(e) built by stacking envelope cells C_(e)(custom built or generated) in series, find the network N_(m) from theset of all possible networks N_(i) of depth L_(i)>L_(e) that may beconstructed by removing n-number of blocks of N_(e) and adding them backin different locations, such that the accuracy Perf is maximized,subject to constraints on network complexity (e.g., number of blocks,parameters and operations M, etc.). Said differently, the goal of thepruning and network restructuring may be formalized as follows:

-   -   Find N_(m) such that Perf(N_(m))>Perf(N_(i)), ∀i | M        (N_(m))<M_(max)

In general, the techniques herein are non-optimal in the sense that theresulting convolutional neural network may not actually be the mostoptimal out of all possible network architectures. However, as describedbelow, the techniques herein do generate networks that exhibit betterperformance than the starting EnvelopeNet and arbitrarily constructednetworks of the same complexity (e.g., same depth, same blocks, andapproximately the same number of parameters).

As noted above, a convolutional neural network may comprise any numberof cells, each of which includes one or more blocks (e.g.,operations/operators). The specific blocks and cells used may differ,depending on the application. For example, FIGS. 3A-3D illustrateexample cells for a convolutional neural network capable of imagerecognition, according to various embodiments. Generally, these cellsinclude an initialization cell 300 in FIG. 3A, a widener cell 310 inFIG. 3B, a classification cell 320 in FIG. 3C, and an envelope cell 330in FIG. 3D.

Initialization cell 300 in FIG. 3A may be located at the start of theconstructed convolutional neural network and may be operable toinitialize the network. As shown, initialization cell 300 may comprisethe following blocks: a 3×3 convolutional filter block 302, followed bya max_pool block 304, and then by another 3×3 convolutional filter block306. As would be appreciated, convolutional filter blocks 302 and 304may perform convolution operations, while max_pool block 304 may performa max pool operation. In general, max pooling is a sample-baseddiscretization process that attempts to down-sample a representation ofan image. Doing so reduces the dimensionality of the imagerepresentation, thereby allowing for the binning of different regions ofthe image for purposes of feature analysis.

Widener cell 310 in FIG. 3B may comprise a single max_pool block 312that reduces the image dimensions by a factor of two and doubles thechannel width. In various embodiments, a copy of widener cell 310 may beplaced at regular intervals, also referred to as a widening factor, inthe neural network. For example, widener cell 310 may be placed in theneural network after every fourth cell, using a widening factor equal tofour.

Classification cell 320 in FIG. 3C may comprise the following blocks inseries: a reduce_mean block 322, a flatten block 324, and afully_connected block 326. In general, reduce_mean block 322 may beoperable to perform an average pooling operation on the representationof the image. Similar to max pooling, average pooling may perform adimensionality reduction on the representation of the image but, asopposed to max pooling whereby the maximum of each bin is taken, averagepooling takes an average of each pixel space. In general, classificationcell 320 may be placed at the tail end of the neural network. Inaddition, no dropout may be applied during construction of the initialneural network. Notably, during experimentation, it was observed thatdropout actually increases the amount of time needed for the variancemetrics to stabilize. Thus, dropout may be disabled, in someembodiments.

Envelope cell 330 in FIG. 3D may be formed using the following blocksconnected in parallel: a 5×5 convolutional filter block 332, a 3×3convolutional filter block 334, a 5×5 separable convolutional filterblock 336, and a 3×3 separable convolutional filter block 338. Each ofblocks 332-338 may comprise a convolution unit, a Relu unit, and a batchnormalization unit, in some cases. As shown, envelope cell 330 may alsoinclude a concatenation block 340 that concatenates the outputs ofblocks 332-338, to form the final output of envelope cell 330. As wouldbe appreciated, envelope cell 330 represents one possible envelope cellconfiguration and the techniques herein can be used to form any numberof different envelope cells with different blocks and/or layouts (e.g.,series or parallel), as desired.

According to various embodiments, the machine learning process may forman EnvelopeNet by stacking a number of envelope cells in series. Thecomplete neural network can then be formed by placing an initializationcell and classification cell at the head and tail of the EnvelopeNet,respectively. Widener cells may be placed at cell intervals within theneural network, according to the specified widener interval. Once thesystem has constructed the initial neural network, the system may trainthe network by iteratively measuring metrics for each of the filters inthe network, pruning the low performing filters from the network basedon their metrics, subject to certain constraints, and appending a newenvelope cell into the network.

A number of different metrics may be measured and used for purposes ofpruning filters from the constructed neural network. These metrics mayinclude, but are not limited to, the mean activation, l₁ norm, entropyor activations and scaled entropy. In a further embodiment, the machinelearning process may prune, at each iteration of the training, thex-number of filters that have the least variance in their featuremaps,computed over a suitably large training dataset. The reasoning for thisis that, after a reasonable amount of training is complete, filtersgenerally identify the scale of the features which they extract. In thisstate, filters which have consistently low variance in the distributionof their output featuremap over the training, are contributingcomparatively less to the output of the classifier. Such filters arecandidate filters for pruning, and may be substituted by other filtersat locations where they may contribute to more information extraction.In other words, the underlying approach attempts to move a lowperforming filter in the neural networks to a different layer placementwhere the filter can contribute more to the classification task.

According to various embodiments, rather than simply rearranging thelocations of poor performing filters in the neural network, thetechniques herein instead propose appending another copy of the envelopecell to the tail of the network. Thus, at each iteration of thetraining, the learning process may remove the x-number of lowestperforming filters and append a new envelope cell onto the deep end ofthe network. Doing so both narrows and deepens the neural network, whilemaintaining the overall network parameter count.

Said differently, the machine learning process may construct and train aconvolutional neural network by performing any or all of the followingsteps:

-   -   1. Form an envelope cell using several operations/blocks, such        as filters, samplers, etc., either in series or parallel. The        envelope cell should be constructed to form an envelope around        the cell architectures used.    -   2. Stack envelope cells to form an EnvelopeNet.    -   3. Train the EnvelopeNet and collect performance metrics (e.g.,        variance metrics) for each of the blocks. Sort the blocks in        order of performance metrics.    -   4. Stop the training once the statistics have stabilized and        remove the n-number of worst performing blocks from the network.        Add n-number of new blocks, in an envelope cell, to the network        (e.g., at the tail end of the network).    -   5. Repeat training on the network.    -   6. Iterate through steps 4 and 5 until the network reaches a        predefined, desired depth.

In greater detail, pseudocode for the techniques herein is as following,in one embodiment:

Function main EnvelopeNetwork   iterations ← 0   network ←EnvelopeNetwork   while iterations < restructureiterations do   //Filter stats are featuremap variances indexed by filter and layer   filterstats ← train(network)    evaluate (network)    network ←construct (network , filterstats)    iterations ← iterations + 1   endend Function construct network, filterstats   //Get cells/layer in orderof variance   sorted filters ← sort(filterstats)   restructure filters ←[ ]   filtercount ← get filtercount(network)   for cell c insortedfilters do    layer ← layer(cell)    ifrestructurefiltercount(layer) + 1 > filtercount(layer)     then     //Donot prune a cell if it is the last cell in the layer     continue    else     restructurefilters.add(cell)     iflength(restructuredfilters) > maxrestructuring      then      //Limitrestructured filters to 4 or other desired threshold      break     else   end   end   //Remove pruned filters and add envelopecell to end  //Add necessary wideners   removefilters(arch, prunedfilters)  addcell(arch, envelopecell) end

FIGS. 4A-4B illustrate the construction and training of a neural networkin accordance with the teachings herein, in various embodiments. Asshown in FIG. 4A, the learning process may construct an initialEnvelopeNet 400 that is six layers deep. Notably, EnvelopeNet 400includes six copies of envelope cell 330 described previously withrespect to FIG. 3D, namely envelope cells 330 a-330 f. Each of envelopecells 330 a-330 f include copies of blocks 330-338 (e.g., convolutionfilter blocks) in parallel, as well as a concatenation block 340 thatconcatenates the outputs of blocks 330-338. Also as shown, assume that awidening factor of 4 is in use. Accordingly, a copy of widener cell 310separates envelope cells 330 d and 330 e, the fourth and fifth envelopecells in EnvelopeNet 400. EnvelopeNet 400 may be referred to as a 6×4-Nnetwork, as it includes six copies of envelope cell 330, each of whichis four blocks deep. In this convention, ‘N’ denotes the number ofiterations that will be used to form the finalized network.

Once the initial EnvelopeNet 400 is constructed, the machine learningprocess may train EnvelopeNet 400 using a training dataset of images.During this training, the process may capture statistics from thefeaturemaps at the outputs of the convolution filter blocks 332-338 inenvelope cells 330 a-330 f. For example, the machine learning processmay compute a running variance of the featuremap elements from thecaptured metrics and use this to compute an average variance for eachfilter block 332-338.

After computing the average variance for each filter block 332-338, themachine learning process may prune the worst performing filter blocksfrom EnvelopeNet 400. For example, the machine learning process may sortthe average variance metrics of the filter blocks 332-338 and identifythe n-number of blocks with the lowest variance metrics. In turn, themachine learning process may prune out these identified blocks 332-338from EnvelopeNet 400. In some embodiments, the machine learning processmay impose a constraint during the pruning that each envelope cell 330must still include at least one filter block.

During each iteration of training, in addition to performing filterblock filtering, the machine learning process may also append a new copyof envelope cell 330 to EnvelopeNet 400. For example, the process mayappend a new copy of envelope cell 330 onto the deepest end ofEnvelopeNet 400. In some embodiments, if a widening factor is specified,the process may also add in a widener cell 310 at the specified cellintervals. The machine learning process may repeat the variance metricgathering, pruning, and envelope cell appending steps, until apredefined number of iterations is reached.

FIG. 4B illustrates an example of EnvelopeNet 400 after five iterationsof processing. As a result of the five rounds of iteration, envelopecells 330 g-330 k were appended onto EnvelopeNet 400, as well as widenercell 310 b, based on a widening factor of 4. During the iterations,certain filter blocks 332-338 were also pruned from EnvelopeNet 400. Forexample, convolution filter blocks 334 a-338 a were pruned from envelopecell 330 a. By constraint, envelope cell 330 a may be required to haveat least one filter block, thereby leaving filter block 332 a as thesole filter block left in this cell. The machine learning process mayalso perform similar pruning of envelope cells 330 b-330 k, pruning outthe filter blocks with the lowest average variance metrics periteration. As a result of the iterations, EnvelopeNet 400 is now aneleven layer deep network. As would be appreciated, EnvelopeNet 400 isshown, but the full convolutional neural network will also include aleading initialization cell 300 and a classification cell 320 on thetail end.

To test the efficacy of the techniques herein, two experiments wereconducted: an analysis of the metric chosen to select the filter blocksto be pruned during the restructuring process and an analysis of theperformance of the restructured network with ablation. The experimentscovered both the construction of the network and the evaluation of theEnvelopeNet and generated network. Training was performed using theCIFAR-10 dataset of images. Both construction and evaluation of thegenerated networks used a common set of hyperparameters which were keptconstant for all runs. The training used preprocessing techniques suchas random cropping, varying brightness and contrast. The optimizationwas RMSProp with momentum=0.9, learning rate=0.01, and an exponentialdecay of 0.94 per 2 epochs. A weight decay with a factor of 4×10⁻⁵ wasalso used. The batch size was set to 50 for all experiments. Nohyperparameter tuning was done on the EnvelopeNet or the generatednetworks. The number of restructuring iterations restructureiterationswas set to 5, the number of training steps for the restructuringalgorithm was set to 30,000, and the number of filters to be pruned periteration was set to maxrestructure=4. Training and evaluation of thebased and generated networks ran for 30-70,000 training steps on anNVIDIA GeForce GTX 980/1080 GPU systems on bare metal and on NVIDIA K80GPU systems running TensorFlow version 1.5.0.

For purposes of testing, the restructuring metric chosen was thevariance of the featuremaps at the output of the filters. The size ofall featuremaps at a given layer was the same, allowing the variance offeaturemaps at different filters to be compared. However, to compare themetric across layers, the per-filter variance needed to be averaged perelement of the featuremap. At every training step, the machine learningprocess collected the counts and sums from the featuremap at the outputof every filter. the machine learning process then used the counts tocalculate a running variance of each element of the featuremap on a perfilter basis. The per-filter, per-element variance was obtained byaveraging over the elements of the featuremap.

As a result of the testing, it was demonstrated that the variances arerelatively constant after 30,000 training iterations, allowing themachine learning process to sort the filters and identify filters forpruning. Note that the variance stabilization at 30,000 iterations, alsoreferred to as the variance stabilization time, is substantially lowerthan the number of iterations required to fully train the network (e.g.,approximately 100,000 iterations).

The variance results above show that the variance metrics of the filterblocks in the network have stabilized after approximately 30,000iterations, allowing for the selection of the filter to be restructuredfairly quickly. The total time for the machine learning process to run Niterations is N times the variance stabilization time. This comparesfavorably with both evolutionary methods, where the run time is afunction of the total number of possible block combinations for anetwork, and cell search methods where the search time is a function ofthe total number of possible block combinations for a cell. At eachiteration, the machine learning process may check the accuracy of theresulting network, to verify that it exceeds the accuracy of theprevious network. If the accuracy drops, the iteration may terminate.However, during experimentation, it was found that the accuracyincreased with each iteration and no premature iterations were observed.

Table 1 below illustrates the number of filters for each layer, theparameters and flops for the 6×4 EnvelopeNet, and the generated network(6×4-5) formed during testing. Table 1 below also shows the parametersfor an “arbitrary” network, namely, a network with the same depth andnumber of filters as the resulting 6×4-5 network, with an arbitrarilychosen structure, referred to as the 6×4-5-Random network (or thearbitrary net).

TABLE 1 Operations Network Number of filters in each layer Parameters(flops) 6 × 4 4, 4, 4, 4, 4, 4 12.18M  7.82 B 6 × 4-5 1, 1, 1, 1, 4, 3,2, 1, 4, 2, 4 16.91M 18.65 B 6 × 4-5-Random 4, 4, 4, 2, 1, 1, 2, 2, 1,2, 1 16.41M 14.47 B

FIG. 5 illustrates an example plot 500 of accuracy test results usingthe techniques herein. As shown, the accuracies of convolutional neuralnetworks were tested for the initial 6×4 EnvelopeNet, the resulting6×4-5 generated network after five iterations of training/networkrearrangement, and for a 6×4-5-Random network with an arbitrarilyselected architecture. The CIFAR-10 dataset was then used to test theaccuracy of each neural network, with plot 500 showing the resultingimage recognition task accuracies vs. number of training iterations usedto train the networks.

From plot 500, it can be seen that the 6×5-5 restructured neural networkoutperforms the neural network based on the initial 6×4 EnvelopeNet by afair amount. The performance of the arbitrary network was also betterthan that of the 6×4 EnvelopeNet-based network, but still lower than thenetwork generated using the techniques herein. This ablation resultindicates that structure of the generated network is responsible forsome of the gain, and that the entire gains do not come from deepeningthe network.

FIG. 6 illustrates an example simplified procedure 600 for training aneural network using envelope cells, in accordance with one or moreembodiments described herein. For example, a non-generic, specificallyconfigured device (e.g., device 200) may perform procedure 600 byexecuting stored instructions (e.g., process 248) to implement a machinelearning process configured to generate a convolutional neural networkcapable of performing image recognition/classification. The procedure600 may start at step 605, and continues to step 610, where, asdescribed in greater detail above, the device may form a neural networkenvelope cell that comprises a plurality of convolution-based filters inseries or parallel. In general, as noted above, such an envelope cellmay include any number of operations/blocks that act as a superset ofoperations/blocks to be applied. In the specific task of imageclassification, such blocks may include convolutional filters. However,other operations/blocks can be used in an envelope cell, in furtherembodiments.

At step 615, as detailed above, the device may a construct convolutionalneural network by stacking copies of the envelope cell in series. Such aseries of envelope cells is also referred to as an EnvelopeNet. In someembodiments, a widener cell may be placed in the network after aspecified number of envelope cells.

According to various embodiments, the device may restructure the neuralnetwork constructed in step 615 by iteratively training the networkusing a training dataset of images, or other training dataset, if thenetwork is to perform a different type of classification. In variousembodiments, the device may perform these iterations a set number oftimes, to produce a finalized convolutional neural network of a desireddepth. For example, five iterations on an initial network of depth sixwill result in a network of depth eleven. In general, as shown, theseiterative steps may include steps 620-630.

At step 620, the device may collect variance metrics for each filter ineach envelope cell of the neural network, during each iteration, asdescribed in greater detail above. Notably, during each iteration, thedevice may train the network using a predefined number of training stepsand, in turn, measure the variances of the featuremaps of the filters inthe neural network. Such variance metrics may be an average of thefeaturemap variances, in some cases. As would be appreciated, othermetrics may be collected and used, in further embodiments.

At step 625, as detailed above, the device may also prune filters withlow variance metrics from the convolutional neural network. For example,during each iteration, the device may prune the n-number of filters inthe network with the lowest average variances. In some embodiments, thedevice may also impose a constraint on the pruning that at least one (ormore than one) filters remain in each envelope cell in the network.

At step 630, the device may append a new copy of the envelope cell intothe convolutional neural network, as described in greater detail above.Notably, during each iteration, the device may add a new copy of theenvelope cell from step 610 to the deep end of the network. In doing so,new filters are added back into the network at a different location, toreplace those pruned in step 625.

Once the device has performed the specified number of iterations ofsteps 620-630, procedure continues on to step 635 and ends. As a resultof the iterations, the resulting neural network will perform itsclassification task (e.g., image recognition) with higher accuracy thanthat of the network initially constructed in step 615 using the copiesof the envelope cells.

The techniques described herein, therefore, introduce a neuralarchitecture construction approach using EnvelopeNets that constructs aneural network from a network of superset cells, called envelope cells,via a restructuring process. Analysis of these techniques shows thatthis approach can identify blocks to be restructured with lesscomputation resources than required for the envelope network to betrained to maximum accuracy. In addition, the disclosed techniques canidentify a network architecture with less compute resources than searchbased construction approaches.

While there have been shown and described illustrative embodiments thatprovide for performing machine learning using EnvelopeNets, it is to beunderstood that various other adaptations and modifications may be madewithin the spirit and scope of the embodiments herein. For example,while certain embodiments are described herein with respect to usingmachine learning models for certain tasks, the models are not limited assuch and may be used for other functions, in other embodiments. Inaddition, while certain protocols are shown, other suitable protocolsmay be used, accordingly.

The foregoing description has been directed to specific embodiments. Itwill be apparent, however, that other variations and modifications maybe made to the described embodiments, with the attainment of some or allof their advantages. For instance, it is expressly contemplated that thecomponents and/or elements described herein can be implemented assoftware being stored on a tangible (non-transitory) computer-readablemedium (e.g., disks/CDs/RAM/EEPROM/etc.) having program instructionsexecuting on a computer, hardware, firmware, or a combination thereof.Accordingly, this description is to be taken only by way of example andnot to otherwise limit the scope of the embodiments herein. Therefore,it is the object of the appended claims to cover all such variations andmodifications as come within the true spirit and scope of theembodiments herein.

What is claimed is:
 1. A method comprising: forming, by a device, aneural network envelope cell that comprises a plurality ofconvolution-based filters in series or parallel; constructing, by thedevice, a convolutional neural network by stacking copies of theenvelope cell in series; and training, by the device and using atraining dataset of images, the convolutional neural network to performimage classification by iteratively: collecting variance metrics foreach filter in each envelope cell; pruning filters with low variancemetrics from the convolutional neural network; and appending a new copyof the envelope cell into the convolutional neural network.
 2. Themethod as in claim 1, further comprising: using the trainedconvolutional neural network to classify an image.
 3. The method as inclaim 1, wherein the envelope cell comprises a plurality of differentconvolution-based filters in parallel and a concatenation operator thatconcatenates outputs of the parallel convolution-based filters.
 4. Themethod as in claim 1, wherein pruning the filters with low variancemetrics from the convolutional neural network comprises: ensuring thatat least one filter remains unpruned from each envelope cell.
 5. Themethod as in claim 1, wherein constructing the convolutional neuralnetwork by stacking copies of the envelope cell in series comprises:adding a maxpool operator in series in the convolutional neural networkafter a predefined number of envelope cells.
 6. The method as in claim1, further comprising: ending the training of the convolutional neuralnetwork after a threshold number of iterations.
 7. The method as inclaim 1, wherein pruning the filters with low variance metrics from theconvolutional neural network comprises: pruning a set number of filterswith the lowest variance metrics from the convolutional neural networkduring each iteration of the training.
 8. An apparatus, comprising: oneor more network interfaces to communicate with a network; a processorcoupled to the network interfaces and configured to execute one or moreprocesses; and a memory configured to store a process executable by theprocessor, the process when executed configured to: form a neuralnetwork envelope cell that comprises a plurality of convolution-basedfilters in series or parallel; construct a convolutional neural networkby stacking copies of the envelope cell in series; and train, using atraining dataset of images, the convolutional neural network to performimage classification by iteratively: collecting variance metrics foreach filter in each envelope cell; pruning filters with low variancemetrics from the convolutional neural network; and appending a new copyof the envelope cell into the convolutional neural network.
 9. Theapparatus as in claim 8, wherein the process when executed is furtherconfigured to: use the trained convolutional neural network to classifyan image.
 10. The apparatus as in claim 8, wherein the envelope cellcomprises a plurality of different convolution-based filters in paralleland a concatenation operator that concatenates outputs of the parallelconvolution-based filters.
 11. The apparatus as in claim 8, wherein theapparatus prunes the filters with low variance metrics from theconvolutional neural network by: ensuring that at least one filterremains unpruned from each envelope cell.
 12. The apparatus as in claim8, wherein the apparatus constructs the convolutional neural network bystacking copies of the envelope cell in series by: adding a maxpooloperator in series in the convolutional neural network after apredefined number of envelope cells.
 13. The apparatus as in claim 8,wherein the process when executed is further configured to: ending thetraining of the convolutional neural network after a threshold number ofiterations.
 14. The apparatus as in claim 8, wherein the apparatusprunes the filters with low variance metrics from the convolutionalneural network by: pruning a set number of filters with the lowestvariance metrics from the convolutional neural network during eachiteration of the training.
 15. A tangible, non-transitory,computer-readable medium storing program instructions that cause adevice to execute a process comprising: forming, by the device, a neuralnetwork envelope cell that comprises a plurality of convolution-basedfilters in series or parallel; constructing, by the device, aconvolutional neural network by stacking copies of the envelope cell inseries; and training, by the device and using a training dataset ofimages, the convolutional neural network to perform image classificationby iteratively: collecting variance metrics for each filter in eachenvelope cell; pruning filters with low variance metrics from theconvolutional neural network; and appending a new copy of the envelopecell into the convolutional neural network.
 16. The computer-readablemedium as in claim 15, wherein the process further comprises: using thetrained convolutional neural network to classify an image.
 17. Thecomputer-readable medium as in claim 15, wherein the envelope cellcomprises a plurality of different convolution-based filters in paralleland a concatenation operator that concatenates outputs of the parallelconvolution-based filters.
 18. The computer-readable medium as in claim15, wherein pruning the filters with low variance metrics from theconvolutional neural network comprises: ensuring that at least onefilter remains unpruned from each envelope cell.
 19. Thecomputer-readable medium as in claim 15, wherein constructing theconvolutional neural network by stacking copies of the envelope cell inseries comprises: adding a maxpool operator in series in theconvolutional neural network after a predefined number of envelopecells.
 20. The computer-readable medium as in claim 15, wherein pruningthe filters with low variance metrics from the convolutional neuralnetwork comprises: pruning a set number of filters with the lowestvariance metrics from the convolutional neural network during eachiteration of the training